Question

How do I find the approximate value of `log_5 20`?

Answer 1

When approximating logarithms, I find it useful more often than not to convert it to exponential form, as it just makes it that much nicer to look at.

To convert a logarithm to exponential form, simply refer to the illustration below:

If you're curious as to how this works, please read this other answer I collaborated on. It should help :)

So if you converted `log_5 20` into exponential form, you'd get:

`5^? = 20`

Now, we can begin making estimates.

We know that `5^2=25` and `5^1=5`, so I'd guess that the answer is somewhere between 1 and 2, but much closer to 2 than 1 (maybe something like 1.8).

And the answer is 1.86. Close enough :)

This is only how to estimate. If you want to get exact answers for tests or quizzes, you should either use the "logBASE" function found on TI-84 calculators, or the change of base formula, for which this video will help:

Hope that helps :)